On the Uncapacitated Plant Location Problem. I: Valid Inequalities and Facets

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Abstract
The uncapacitated plant location problem is considered as a node-packing problem. For this problem, several valid inequalities and facets are discussed. Necessary and sufficient conditions for trivial facets along with necessary conditions for nontrivial facets are derived. In addition, all of the facets for the case of three plants and three or more destinations are identified.